import pandas as pd

# Loading the dataset
file_path = 'path_to_dataset.csv'  # Replace with your file path
data = pd.read_csv("ObesityDataSet_raw_and_data_sinthetic.csv")

# Displaying the first few rows and data set information
data_info = data.info()
data_head = data.head()

data_info
data_head

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 2111 entries, 0 to 2110
Data columns (total 17 columns):
 #   Column                          Non-Null Count  Dtype  
---  ------                          --------------  -----  
 0   Gender                          2111 non-null   object 
 1   Age                             2111 non-null   float64
 2   Height                          2111 non-null   float64
 3   Weight                          2111 non-null   float64
 4   family_history_with_overweight  2111 non-null   object 
 5   FAVC                            2111 non-null   object 
 6   FCVC                            2111 non-null   float64
 7   NCP                             2111 non-null   float64
 8   CAEC                            2111 non-null   object 
 9   SMOKE                           2111 non-null   object 
 10  CH2O                            2111 non-null   float64
 11  SCC                             2111 non-null   object 
 12  FAF                             2111 non-null   float64
 13  TUE                             2111 non-null   float64
 14  CALC                            2111 non-null   object 
 15  MTRANS                          2111 non-null   object 
 16  NObeyesdad                      2111 non-null   object 
dtypes: float64(8), object(9)
memory usage: 280.5+ KB

# Checking for missing values in each column
missing_values = data.isnull().sum()
print(missing_values)

Gender                            0
Age                               0
Height                            0
Weight                            0
family_history_with_overweight    0
FAVC                              0
FCVC                              0
NCP                               0
CAEC                              0
SMOKE                             0
CH2O                              0
SCC                               0
FAF                               0
TUE                               0
CALC                              0
MTRANS                            0
NObeyesdad                        0
dtype: int64

# Checking for duplicates
duplicates = data.duplicated().sum()

# Printing duplicates count
print(duplicates)

# Removing the duplicates
data = data.drop_duplicates()

24

# Displaying summary statistics and Checking for outliers in continuous variables (e.g., Age, Weight, Height)
data.describe()

from sklearn.preprocessing import LabelEncoder, OneHotEncoder, MinMaxScaler

# Copying the dataset to ensure the original remains intact
transformed_data = data.copy()

# Label Encoding for binary and ordinal variables
label_encoder = LabelEncoder()

binary_features = ['family_history_with_overweight', 'FAVC', 'SMOKE', 'SCC']
target_variable = 'NObeyesdad'

for feature in binary_features:
    transformed_data[feature] = label_encoder.fit_transform(transformed_data[feature])

# Label encoding the target variable (Ordinal Relationship Exists)
transformed_data[target_variable] = label_encoder.fit_transform(transformed_data[target_variable])

# One-Hot Encoding for nominal variables
nominal_features = ['Gender', 'CAEC', 'CALC', 'MTRANS']
transformed_data = pd.get_dummies(transformed_data, columns=nominal_features, drop_first=True)

# Scaling the continuous features using Min-Max Scaling
scaler = MinMaxScaler()

continuous_features = ['Age', 'Height', 'Weight', 'FCVC', 'NCP', 'CH2O', 'FAF', 'TUE']
transformed_data[continuous_features] = scaler.fit_transform(transformed_data[continuous_features])

# Displaying Transformed Dataset after pre-processing
transformed_data.head()

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from scipy.stats import mode

# Univariate Analysis

# Summary statistics for numerical variables
summary_stats = transformed_data.describe().T
summary_stats['mode'] = transformed_data[continuous_features].mode().iloc[0]
summary_stats = summary_stats[['mean', '50%', 'std', 'min', 'max', 'mode']]
summary_stats.rename(columns={'50%': 'median'}, inplace=True)

# Frequency distribution for categorical variables
categorical_features = [
    col for col in transformed_data.columns
    if transformed_data[col].nunique() <= 10 and col not in ['NObeyesdad']
]
freq_distribution = {}
for col in categorical_features:
    freq_distribution[col] = transformed_data[col].value_counts()

# Plotting Histograms and Box Plots for numerical variables
for feature in continuous_features:
    # Histogram with Density
    plt.figure(figsize=(10, 5))
    sns.histplot(transformed_data[feature], kde=True, bins=20, color='blue', alpha=0.6)
    plt.title(f"Histogram and Density Plot for {feature}")
    plt.xlabel(feature)
    plt.ylabel("Frequency")
    plt.show()
    
    # Box Plot
    plt.figure(figsize=(10, 5))
    sns.boxplot(x=transformed_data[feature], color='green')
    plt.title(f"Box Plot for {feature}")
    plt.xlabel(feature)
    plt.show()

# Displaying summary statistics and frequency distributions
print(summary_stats)

# Frequency distributions for categorical variables
print(freq_distribution)

                                    mean    median       std  min  max  \
Age                             0.220279  0.188247  0.135506  0.0  1.0   
Height                          0.476744  0.474687  0.175823  0.0  1.0   
Weight                          0.357155  0.329113  0.195454  0.0  1.0   
family_history_with_overweight  0.825108  1.000000  0.379966  0.0  1.0   
FAVC                            0.883565  1.000000  0.320823  0.0  1.0   
FCVC                            0.710733  0.698133  0.267368  0.0  1.0   
NCP                             0.567060  0.666667  0.254871  0.0  1.0   
SMOKE                           0.021083  0.000000  0.143695  0.0  1.0   
CH2O                            0.502375  0.500000  0.304142  0.0  1.0   
SCC                             0.045999  0.000000  0.209533  0.0  1.0   
FAF                             0.337604  0.333333  0.284492  0.0  1.0   
TUE                             0.331518  0.315433  0.304077  0.0  1.0   
NObeyesdad                      3.014375  3.000000  1.948470  0.0  6.0   

                                    mode  
Age                             0.085106  
Height                          0.471698  
Weight                          0.305970  
family_history_with_overweight       NaN  
FAVC                                 NaN  
FCVC                            1.000000  
NCP                             0.666667  
SMOKE                                NaN  
CH2O                            0.500000  
SCC                                  NaN  
FAF                             0.000000  
TUE                             0.000000  
NObeyesdad                           NaN  
{'family_history_with_overweight': family_history_with_overweight
1    1722
0     365
Name: count, dtype: int64, 'FAVC': FAVC
1    1844
0     243
Name: count, dtype: int64, 'SMOKE': SMOKE
0    2043
1      44
Name: count, dtype: int64, 'SCC': SCC
0    1991
1      96
Name: count, dtype: int64, 'Gender_Male': Gender_Male
True     1052
False    1035
Name: count, dtype: int64, 'CAEC_Frequently': CAEC_Frequently
False    1851
True      236
Name: count, dtype: int64, 'CAEC_Sometimes': CAEC_Sometimes
True     1761
False     326
Name: count, dtype: int64, 'CAEC_no': CAEC_no
False    2050
True       37
Name: count, dtype: int64, 'CALC_Frequently': CALC_Frequently
False    2017
True       70
Name: count, dtype: int64, 'CALC_Sometimes': CALC_Sometimes
True     1380
False     707
Name: count, dtype: int64, 'CALC_no': CALC_no
False    1451
True      636
Name: count, dtype: int64, 'MTRANS_Bike': MTRANS_Bike
False    2080
True        7
Name: count, dtype: int64, 'MTRANS_Motorbike': MTRANS_Motorbike
False    2076
True       11
Name: count, dtype: int64, 'MTRANS_Public_Transportation': MTRANS_Public_Transportation
True     1558
False     529
Name: count, dtype: int64, 'MTRANS_Walking': MTRANS_Walking
False    2032
True       55
Name: count, dtype: int64}

import matplotlib.pyplot as plt
import seaborn as sns

# Bivariate Analysis

# Set style for better visualization
sns.set(style="whitegrid")

# Scatter plots for continuous variables vs. target variable
continuous_features = ['Age', 'Height', 'Weight', 'FCVC', 'NCP', 'CH2O', 'FAF', 'TUE']
target_variable = 'NObeyesdad'

# Creating scatter plots for continuous features against the target
for feature in continuous_features:
    plt.figure(figsize=(8, 6))
    sns.scatterplot(data=transformed_data, x=feature, y=target_variable, alpha=0.7)
    plt.title(f"{feature} vs. {target_variable}")
    plt.xlabel(feature)
    plt.ylabel("Obesity Level")
    plt.show()

# Correlation Matrix for Continuous Features
plt.figure(figsize=(12, 8))
correlation_matrix = transformed_data[continuous_features].corr()
sns.heatmap(correlation_matrix, annot=True, cmap="coolwarm", fmt=".2f")
plt.title("Correlation Matrix for Continuous Features")
plt.show()

# Pair Plot to visualize pairwise relationships
sns.pairplot(transformed_data[continuous_features + [target_variable]], diag_kind="kde", hue=target_variable)
plt.show()

from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler

# Multivariate Analysis

# Heatmap for full dataset correlation (continuous features and encoded categorical variables)
plt.figure(figsize=(16, 12))
sns.heatmap(transformed_data.corr(), annot=False, cmap="coolwarm")
plt.title("Correlation Heatmap (All Features)")
plt.show()

# Dimensionality Reduction with PCA
# Standardizing the dataset for PCA
scaler = StandardScaler()
scaled_data = scaler.fit_transform(transformed_data)

# Applying PCA to reduce to 2 principal components for visualization
pca = PCA(n_components=2)
pca_result = pca.fit_transform(scaled_data)

# Adding PCA results back to the dataframe for plotting
transformed_data['PCA1'] = pca_result[:, 0]
transformed_data['PCA2'] = pca_result[:, 1]

# Scatter plot of the first two principal components
plt.figure(figsize=(10, 8))
sns.scatterplot(data=transformed_data, x='PCA1', y='PCA2', hue='NObeyesdad', alpha=0.7, palette="viridis")
plt.title("PCA: First Two Principal Components")
plt.xlabel("Principal Component 1")
plt.ylabel("Principal Component 2")
plt.legend(title="Obesity Levels")
plt.show()

# Pairwise relationships with a subset of features for clarity
pairwise_features = ['Age', 'Weight', 'FAF', 'TUE', 'NObeyesdad']
sns.pairplot(transformed_data[pairwise_features], hue='NObeyesdad', diag_kind="kde", palette="viridis")
plt.show()

# 5.1 Linear Regression

from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error, r2_score
import numpy as np

# Selecting a single predictor variable for simple linear regression
predictor = 'Weight'  # Example predictor
target = 'NObeyesdad'  # Target variable

# Split the data into training and testing sets
X = transformed_data[[predictor]]
y = transformed_data[target]
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Initialize and fit the linear regression model
linear_model = LinearRegression()
linear_model.fit(X_train, y_train)

# Predicting on test data
y_pred = linear_model.predict(X_test)

# Calculating R2 and RMSE
r2 = r2_score(y_test, y_pred)
rmse = np.sqrt(mean_squared_error(y_test, y_pred))

# Visualizing the regression line
plt.figure(figsize=(8, 6))
plt.scatter(X_test, y_test, color='blue', alpha=0.6, label='Actual')
plt.plot(X_test, y_pred, color='red', linewidth=2, label='Predicted (Regression Line)')
plt.title(f'Simple Linear Regression: {predictor} vs {target}')
plt.xlabel(predictor)
plt.ylabel(target)
plt.legend()
plt.show()

# Visualizing residuals
residuals = y_test - y_pred
plt.figure(figsize=(8, 6))
plt.scatter(y_pred, residuals, alpha=0.6, color='purple')
plt.axhline(y=0, color='red', linestyle='--', linewidth=2)
plt.title('Residuals of Simple Linear Regression')
plt.xlabel('Predicted Values')
plt.ylabel('Residuals')
plt.show()

# Performance metrics
print(f"Root Mean Squared Error (RMSE): {rmse:.2f}")
print(f"R-squared (R2): {r2:.2f}")

Root Mean Squared Error (RMSE): 1.76
R-squared (R2): 0.17

# 5.2 Multiple Linear Regression

from statsmodels.api import OLS, add_constant

# Selecting multiple predictor variables for multiple linear regression
predictors = ['Weight', 'Height', 'Age', 'FCVC', 'CH2O', 'FAF', 'TUE']
target = 'NObeyesdad'

# Splitting the data into features (X) and target (y)
X = transformed_data[predictors]
y = transformed_data[target]

# Adding a constant term for the intercept in the regression model
X_with_constant = add_constant(X)

# Splitting into training and testing datasets
X_train, X_test, y_train, y_test = train_test_split(X_with_constant, y, test_size=0.2, random_state=42)

# Fitting the multiple linear regression model using statsmodels
model = OLS(y_train, X_train).fit()

# Predicting on the test dataset
y_pred = model.predict(X_test)

# Evaluating the model
r2 = r2_score(y_test, y_pred)
rmse = np.sqrt(mean_squared_error(y_test, y_pred))

# Analyzing the significance of predictor variables (summary of the model)
model_summary = model.summary()

# Displaying the performance metrics
print(f"Root Mean Squared Error (RMSE): {rmse:.2f}")
print(f"R-squared (R2): {r2:.2f}")
print(model_summary)

Root Mean Squared Error (RMSE): 1.68
R-squared (R2): 0.24
                            OLS Regression Results                            
==============================================================================
Dep. Variable:             NObeyesdad   R-squared:                       0.197
Model:                            OLS   Adj. R-squared:                  0.194
Method:                 Least Squares   F-statistic:                     58.27
Date:                Tue, 26 Nov 2024   Prob (F-statistic):           6.63e-75
Time:                        20:02:20   Log-Likelihood:                -3300.0
No. Observations:                1669   AIC:                             6616.
Df Residuals:                    1661   BIC:                             6659.
Df Model:                           7                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          2.2739      0.213     10.683      0.000       1.856       2.691
Weight         4.2937      0.271     15.821      0.000       3.761       4.826
Height        -1.6955      0.303     -5.599      0.000      -2.289      -1.102
Age            1.9613      0.341      5.744      0.000       1.292       2.631
FCVC          -0.6502      0.169     -3.837      0.000      -0.983      -0.318
CH2O           0.3615      0.148      2.436      0.015       0.070       0.653
FAF           -0.3541      0.165     -2.147      0.032      -0.678      -0.031
TUE            0.0467      0.150      0.312      0.755      -0.247       0.341
==============================================================================
Omnibus:                      446.705   Durbin-Watson:                   1.960
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              223.075
Skew:                           0.752   Prob(JB):                     3.63e-49
Kurtosis:                       2.027   Cond. No.                         14.7
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

# 5.3 Polynomial Regression
from sklearn.preprocessing import PolynomialFeatures
from sklearn.pipeline import make_pipeline

# Selecting predictor and target variables for polynomial regression
predictor = 'Weight'  # Example predictor for simplicity
target = 'NObeyesdad'

# Preparing the data
X = transformed_data[[predictor]]
y = transformed_data[target]

# Splitting the data into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Applying Polynomial Regression with degree 2
degree = 2
polynomial_model = make_pipeline(PolynomialFeatures(degree), LinearRegression())
polynomial_model.fit(X_train, y_train)

# Predicting on test data
y_pred_poly = polynomial_model.predict(X_test)

# Evaluating the Polynomial Regression Model
r2_poly = r2_score(y_test, y_pred_poly)
rmse_poly = np.sqrt(mean_squared_error(y_test, y_pred_poly))

# Comparing Polynomial Regression with Linear Regression
# Reusing the previously trained linear regression model for comparison
linear_model.fit(X_train, y_train)
y_pred_linear = linear_model.predict(X_test)
r2_linear = r2_score(y_test, y_pred_linear)
rmse_linear = np.sqrt(mean_squared_error(y_test, y_pred_linear))

# Visualizing Polynomial Regression vs Linear Regression
plt.figure(figsize=(8, 6))
plt.scatter(X_test, y_test, color='blue', alpha=0.6, label='Actual')
plt.scatter(X_test, y_pred_poly, color='green', alpha=0.6, label='Polynomial Predictions')
plt.plot(X_test, y_pred_linear, color='red', linewidth=2, label='Linear Regression Line')
plt.title(f'Polynomial Regression (Degree {degree}) vs Linear Regression')
plt.xlabel(predictor)
plt.ylabel(target)
plt.legend()
plt.show()

# Displaying the performance metrics
print(f"Polynomial Regression - Root Mean Squared Error (RMSE): {rmse_poly:.2f}")
print(f"Polynomial Regression - R-squared (R2): {r2_poly:.2f}")

print(f"Linear Regression - Root Mean Squared Error (RMSE): {rmse_linear:.2f}")
print(f"Linear Regression - R-squared (R2): {r2_linear:.2f}")

Polynomial Regression - Root Mean Squared Error (RMSE): 1.58
Polynomial Regression - R-squared (R2): 0.33
Linear Regression - Root Mean Squared Error (RMSE): 1.76
Linear Regression - R-squared (R2): 0.17

# 5.4 Logistic Regression
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import accuracy_score, precision_score, recall_score, roc_auc_score, roc_curve

# Preparing the data for logistic regression
# Simplifying the task to binary classification: Normal Weight vs Others
transformed_data['BinaryTarget'] = transformed_data['NObeyesdad'].apply(lambda x: 1 if x == 2 else 0)  # Example binary encoding

X = transformed_data[predictors]  # Using multiple predictors
y = transformed_data['BinaryTarget']

# Splitting into training and testing datasets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Training the Logistic Regression model
logistic_model = LogisticRegression(max_iter=1000)
logistic_model.fit(X_train, y_train)

# Making the predictions
y_pred = logistic_model.predict(X_test)
y_pred_prob = logistic_model.predict_proba(X_test)[:, 1]

# Evaluating the model
accuracy = accuracy_score(y_test, y_pred)
precision = precision_score(y_test, y_pred)
recall = recall_score(y_test, y_pred)
roc_auc = roc_auc_score(y_test, y_pred_prob)

# Displaying the Results
print(f"Accuracy: {accuracy:.2f}")
print(f"Precision: {precision:.2f}")
print(f"Recall: {recall:.2f}")
print(f"ROC-AUC: {roc_auc:.2f}")

# Plotting the ROC curve
fpr, tpr, thresholds = roc_curve(y_test, y_pred_prob)
plt.figure(figsize=(8, 6))
plt.plot(fpr, tpr, label=f'Logistic Regression (AUC = {roc_auc:.2f})')
plt.plot([0, 1], [0, 1], 'k--', label='Random Chance')
plt.title('ROC Curve')
plt.xlabel('False Positive Rate')
plt.ylabel('True Positive Rate')
plt.legend()
plt.show()

Accuracy: 0.83
Precision: 0.50
Recall: 0.01
ROC-AUC: 0.79

# 5.5 Regularization Techniques

from sklearn.linear_model import Ridge, Lasso, ElasticNet
from sklearn.model_selection import cross_val_score

# Regularization models - Ridge Regression, Lasso Regression, Elastic Net Regression
ridge_model = Ridge(alpha=1.0)
lasso_model = Lasso(alpha=0.01, max_iter=10000)
elastic_net_model = ElasticNet(alpha=0.01, l1_ratio=0.5, max_iter=10000)

# Performing cross-validation to evaluate each model
ridge_scores = cross_val_score(ridge_model, X, y, cv=5, scoring='r2')
lasso_scores = cross_val_score(lasso_model, X, y, cv=5, scoring='r2')
elastic_net_scores = cross_val_score(elastic_net_model, X, y, cv=5, scoring='r2')

# Training models on full training data
ridge_model.fit(X_train, y_train)
lasso_model.fit(X_train, y_train)
elastic_net_model.fit(X_train, y_train)

# Predicting on the test set
ridge_pred = ridge_model.predict(X_test)
lasso_pred = lasso_model.predict(X_test)
elastic_net_pred = elastic_net_model.predict(X_test)

# Evaluating models
ridge_rmse = np.sqrt(mean_squared_error(y_test, ridge_pred))
lasso_rmse = np.sqrt(mean_squared_error(y_test, lasso_pred))
elastic_net_rmse = np.sqrt(mean_squared_error(y_test, elastic_net_pred))

ridge_r2 = r2_score(y_test, ridge_pred)
lasso_r2 = r2_score(y_test, lasso_pred)
elastic_net_r2 = r2_score(y_test, elastic_net_pred)

# Printing the performance comparison
print("Performance Comparison of Regularization Techniques:")
print(f"Ridge Regression:    R2 = {ridge_r2:.2f}, RMSE = {ridge_rmse:.2f}, CV Mean R2 = {ridge_scores.mean():.3f}")
print(f"Lasso Regression:    R2 = {lasso_r2:.2f}, RMSE = {lasso_rmse:.2f}, CV Mean R2 = {lasso_scores.mean():.3f}")
print(f"Elastic Net:         R2 = {elastic_net_r2:.2f}, RMSE = {elastic_net_rmse:.2f}, CV Mean R2 = {elastic_net_scores.mean():.3f}")

Performance Comparison of Regularization Techniques:
Ridge Regression:    R2 = 0.12, RMSE = 0.35, CV Mean R2 = -0.809
Lasso Regression:    R2 = 0.03, RMSE = 0.37, CV Mean R2 = -1.124
Elastic Net:         R2 = 0.06, RMSE = 0.36, CV Mean R2 = -1.128

# 5.6 Quantile Regression
import statsmodels.api as sm
import numpy as np

# Selecting predictor and target for quantile regression
predictor = 'Weight'  # Example predictor
target = 'NObeyesdad'

X = transformed_data[[predictor]]
y = transformed_data[target]

# Adding a constant for the intercept
X_with_const = sm.add_constant(X)

# Quantiles to predict
quantiles = [0.1, 0.5, 0.9]

# Fitting quantile regression models
quantile_models = {}
for q in quantiles:
    quantile_model = sm.QuantReg(y, X_with_const).fit(q=q)
    quantile_models[q] = quantile_model
    print(f"Quantile {q}:")
    print(quantile_model.summary())

# Plotting the regression lines for different quantiles
plt.figure(figsize=(8, 6))
plt.scatter(X, y, alpha=0.5, label='Data', color='gray')

# Predict for the quantile lines
x_range = np.linspace(X[predictor].min(), X[predictor].max(), 100)
x_range_with_const = sm.add_constant(pd.DataFrame({predictor: x_range}))

for q, quantile_model in quantile_models.items():
    y_quantile = quantile_model.predict(x_range_with_const)
    plt.plot(x_range, y_quantile, label=f'Quantile {q}', linewidth=2)

plt.title('Quantile Regression Lines')
plt.xlabel(predictor)
plt.ylabel(target)
plt.legend()
plt.show()

Quantile 0.1:
                         QuantReg Regression Results                          
==============================================================================
Dep. Variable:             NObeyesdad   Pseudo R-squared:               0.3894
Model:                       QuantReg   Bandwidth:                      0.6117
Method:                 Least Squares   Sparsity:                        2.808
Date:                Tue, 26 Nov 2024   No. Observations:                 2087
Time:                        20:12:47   Df Residuals:                     2085
                                        Df Model:                            1
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const         -0.4903      0.041    -11.913      0.000      -0.571      -0.410
Weight         5.1766      0.103     50.258      0.000       4.975       5.379
==============================================================================
Quantile 0.5:
                         QuantReg Regression Results                          
==============================================================================
Dep. Variable:             NObeyesdad   Pseudo R-squared:               0.1759
Model:                       QuantReg   Bandwidth:                      0.7470
Method:                 Least Squares   Sparsity:                        2.692
Date:                Tue, 26 Nov 2024   No. Observations:                 2087
Time:                        20:12:47   Df Residuals:                     2085
                                        Df Model:                            1
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          0.3435      0.061      5.596      0.000       0.223       0.464
Weight         5.1645      0.151     34.252      0.000       4.869       5.460
==============================================================================
Quantile 0.9:
                         QuantReg Regression Results                          
==============================================================================
Dep. Variable:             NObeyesdad   Pseudo R-squared:             0.007249
Model:                       QuantReg   Bandwidth:                      0.6117
Method:                 Least Squares   Sparsity:                        6.071
Date:                Tue, 26 Nov 2024   No. Observations:                 2087
Time:                        20:12:47   Df Residuals:                     2085
                                        Df Model:                            1
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          6.9793      0.055    127.408      0.000       6.872       7.087
Weight        -3.2741      0.107    -30.704      0.000      -3.483      -3.065
==============================================================================

# Model evaluation summary across all methods used
evaluation_metrics = {
    "Linear Regression": {"R2": r2_linear, "RMSE": rmse_linear},
    "Polynomial Regression": {"R2": r2_poly, "RMSE": rmse_poly},
    "Ridge Regression": {"R2": ridge_r2, "RMSE": ridge_rmse},
    "Lasso Regression": {"R2": lasso_r2, "RMSE": lasso_rmse},
    "Elastic Net Regression": {"R2": elastic_net_r2, "RMSE": elastic_net_rmse}
}

# Displaying the metrics comparison as a DataFrame for clarity
evaluation_df = pd.DataFrame(evaluation_metrics).T

# Visualizing model performance comparison
plt.figure(figsize=(12, 6))
evaluation_df['R2'].plot(kind='bar', color='skyblue', alpha=0.8, label='R2 Score')
plt.axhline(0, color='gray', linestyle='--', linewidth=1)
plt.title('R2 Score Comparison Across Models')
plt.ylabel('R2 Score')
plt.legend()
plt.show()

plt.figure(figsize=(12, 6))
evaluation_df['RMSE'].plot(kind='bar', color='salmon', alpha=0.8, label='RMSE')
plt.axhline(0, color='gray', linestyle='--', linewidth=1)
plt.title('RMSE Comparison Across Models')
plt.ylabel('Root Mean Squared Error')
plt.legend()
plt.show()

# Displaying evaluation metrics for interpretation
evaluation_df.head()

	Age	Height	Weight	FCVC	NCP	CH2O	FAF	TUE
count	2087.000000	2087.000000	2087.000000	2087.000000	2087.000000	2087.000000	2087.000000	2087.000000
mean	24.353090	1.702674	86.858730	2.421466	2.701179	2.004749	1.012812	0.663035
std	6.368801	0.093186	26.190847	0.534737	0.764614	0.608284	0.853475	0.608153
min	14.000000	1.450000	39.000000	1.000000	1.000000	1.000000	0.000000	0.000000
25%	19.915937	1.630178	66.000000	2.000000	2.697467	1.590922	0.124505	0.000000
50%	22.847618	1.701584	83.101100	2.396265	3.000000	2.000000	1.000000	0.630866
75%	26.000000	1.769491	108.015907	3.000000	3.000000	2.466193	1.678102	1.000000
max	61.000000	1.980000	173.000000	3.000000	4.000000	3.000000	3.000000	2.000000

	R2	RMSE
Linear Regression	0.172825	1.756740
Polynomial Regression	0.334466	1.575774
Ridge Regression	0.118638	0.350542
Lasso Regression	0.032911	0.367194
Elastic Net Regression	0.062974	0.361442

Comprehensive Regression Analysis & Modeling - "Predicting Obesity Levels"¶

1. Introduction¶

Overview of the project:¶

Objectives:¶

Research Questions:¶

2. Dataset Selection and Description¶

Source of the Dataset:¶

Description of Variables:¶

3. Data Pre-Processing¶

4. Exploratory Data Analysis (EDA)¶

5. Regression Analysis¶

Linear Regression¶

Multiple Linear Regression¶

Polynomial Regression¶

Logistic Refression¶

Regularization Techniques¶

Advanced Regression Techniques¶

Quantile Regression¶

6. Model Evaluation and Comparision¶

7. Results and Interpretation¶

Summary of Findings¶

Insights¶

Limitations¶

8. References¶

	Gender	Age	Height	Weight	family_history_with_overweight	FAVC	FCVC	NCP	CAEC	SMOKE	CH2O	SCC	FAF	TUE	CALC	MTRANS	NObeyesdad
0	Female	21.0	1.62	64.0	yes	no	2.0	3.0	Sometimes	no	2.0	no	0.0	1.0	no	Public_Transportation	Normal_Weight
1	Female	21.0	1.52	56.0	yes	no	3.0	3.0	Sometimes	yes	3.0	yes	3.0	0.0	Sometimes	Public_Transportation	Normal_Weight
2	Male	23.0	1.80	77.0	yes	no	2.0	3.0	Sometimes	no	2.0	no	2.0	1.0	Frequently	Public_Transportation	Normal_Weight
3	Male	27.0	1.80	87.0	no	no	3.0	3.0	Sometimes	no	2.0	no	2.0	0.0	Frequently	Walking	Overweight_Level_I
4	Male	22.0	1.78	89.8	no	no	2.0	1.0	Sometimes	no	2.0	no	0.0	0.0	Sometimes	Public_Transportation	Overweight_Level_II

	Age	Height	Weight	family_history_with_overweight	FCVC	NCP	SMOKE	CH2O	SCC	...	CAEC_Frequently	CAEC_Sometimes	CAEC_no	CALC_Frequently	CALC_Sometimes	CALC_no	MTRANS_Bike	MTRANS_Motorbike	MTRANS_Public_Transportation	MTRANS_Walking
0	0.148936	0.320755	0.186567	1	0.5	0.666667	0	0.5	0	...	False	True	False	False	False	True	False	False	True	False
1	0.148936	0.132075	0.126866	1	1.0	0.666667	1	1.0	1	...	False	True	False	False	True	False	False	False	True	False
2	0.191489	0.660377	0.283582	1	0.5	0.666667	0	0.5	0	...	False	True	False	True	False	False	False	False	True	False
3	0.276596	0.660377	0.358209	0	1.0	0.666667	0	0.5	0	...	False	True	False	True	False	False	False	False	False	True
4	0.170213	0.622642	0.379104	0	0.5	0.000000	0	0.5	0	...	False	True	False	False	True	False	False	False	True	False